Timeline for Does surface integral preserve the curl operation?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2023 at 3:21 | vote | accept | MrPie | ||
| Feb 17, 2023 at 3:19 | comment | added | MrPie | lol @losifpinelis you already wrapped it up what am I supposed to click delete or something. | |
| Feb 17, 2023 at 2:41 | comment | added | Iosif Pinelis | @MrPie : Your question was "Does the surface integral of $\textbf{n}\times\textbf{F}$ commute with the curl operation [...]?" This is a yes-or-no question, and it was fully answered. Your additional question concerning a non-curl-free field was answered as well. So, please let us wrap it up. | |
| Feb 16, 2023 at 23:01 | comment | added | MrPie | @Losifpinels Thanks, I think you proved the inequality is not true in general. Maybe it holds for specific type of vector fields. But this could get complicated to find which vector fields this could be (if there are any at all) | |
| Feb 16, 2023 at 22:56 | comment | added | Iosif Pinelis | @MrPie : Let us wrap it up with the current question, and then I will look at the newer one. | |
| Feb 16, 2023 at 22:54 | comment | added | MrPie | @losifPinelis hmmm interesting thank you!! I posted another question related to this topic if you're interested. It is here mathoverflow.net/questions/441022/… | |
| Feb 16, 2023 at 22:49 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 16, 2023 at 22:43 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 23 characters in body
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| Feb 16, 2023 at 22:31 | comment | added | Iosif Pinelis | @MrPie : This is easy. Take your favorite non-curl-free field $\mathbf G$, and replace my curl-free $\mathbf F$ by $\mathbf F_\delta:=\mathbf F+\delta\,\mathbf G$ with a nonzero real $\delta$. Then $\mathbf F_\delta$ is not curl free, but, by continuity, your identity will still fail to hold with $\mathbf F_\delta$ in place of $\mathbf F$ if $|\delta|$ is small enough. | |
| Feb 16, 2023 at 22:22 | comment | added | MrPie | @losifPinelis sorry I meant if $\textbf{F}$ is not curl free. The contradiction you found was easy because the right hand side vanished quickly but the left doesn't. Can you find such a field with $\textbf{Curl}(\textbf{F})\neq 0$ that still makes this a contradiction? is it true otherwise? | |
| Feb 16, 2023 at 22:17 | comment | added | Iosif Pinelis | @MrPie : I don't understand the point of your question. In my example, $\mathbf F$ is curl free. | |
| Feb 16, 2023 at 21:43 | comment | added | MrPie | @losifPinelis what if $\textbf{F}$ is curl free? It seems that has an impact on this question. | |
| Feb 16, 2023 at 20:36 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |